MatSc503 Kinetics of Materials Processes - Test 1 February 24, 1999 1. (35 points) The phase diagram of a binary system (components A and B) is shown in the figure below. An infinite couple is made wi
Solution to Problem #7 of Sample Exam Questions 7. In CaF2 , the predominant ionic defects are the anti-Frenkel defects whose concentrations are controlled from the following defect reaction:
FF V F
Solutions to Test 1 MatSc 503 - Kinetics of Materials Processes Test date: February 25, 2002
1. A 1-mm-thick sheet of steel at 750C is subjected to conditions that maintain the carbon content at zero
Sample Exam Questions
1. A piece of Steidlium (St) with a dimension 10cm 10cm 1cm containing 1.0 at % Deikium (De) is put into an oven for removing De. The density of St is 5g/cm3. The surface concent
Kinetics of Phase Transformations
(References: J. W. Christian, Theory of Transformations in Metals and Alloys; Porter and Easterling, Phase Transformations in Metals and Alloys)
Change of state, e.g.
Coupling of Other Processes with Diffusion
Review of irreversible thermodynamics Generalized linear theory for coupled kinetic processes Thermoelectric phenomena Thermomigration Electromigration Diff
Self-Diffusion Through Vacancy Mechanism
Self-diffusion: diffusion of atoms in a pure material (e.g., Al atoms in pure Al) or binary and multicomponent compounds in which the diffusion of different at
(e) Electrons, holes, and ionization states of defects The process of forming intrinsic electron-hole pairs is excitation across the bandgap
null e'+ h
Their concentrations can be approximated as
E n
Kirkendall Effect and Chemical Diffusion
Up to this point, we have considered self-diffusion, tracer atom diffusion, and diffusion of small interstitial atoms in a host lattice of larger atoms. We usu
Since the activation for diffusion along extended defects is smaller than that in the bulk, the diffusion along extended defects become increasingly important as temperature decreases Example lnD
Poly
Diffusion in Homogeneous Concentrated Alloys
In a homogeneous concentrated alloy, two tracer diffusion coefficients can be defined, one for each species:
AB DA*
and
AB DB*
They can be measured through
Thermodynamic Properties of Point Defects
(a) Single vacancy in elementary crystals The enthalpy (energy for constant volume) change by removing an atom inside a crystal and placing it on the surface
Atomic Theory of Diffusion
(See Chapter 2 in Philibert)
The purpose: to relate the phenomenological diffusion coefficient to microscopic parameters such as jump distance and jump frequency Consider a
At short times, many terms are required for obtaining the accurate concentration profile. However, at long times, a single term is sufficient as each successive term is smaller than the preceding one.
Square Root Relationship
For infinite or semi-infinite systems with constant surface concentration, the solution involves only the single dimensionless parameter
x 2 Dt
1. 2. 3. The distance of penetr
(2) Extended initial distributions, e.g., for the initial condition, c
c for x < 0 c( x,0 ) = o 0 for x > 0
co
d
x=0 x
Consider a line source of strength, co d
2 co d 1 2 exp 2(Dt ) 4 Dt
Superpositio
Types of Solutions to Ficks Second Law
Error function solutions short-time or infinite systems
l (system size ) > Dt
Trigonometric function solutions long-time or finite systems
l (system size ) ~ Dt
Numerical Example Quasi-steady State
A cubic steel tank of volume 1 liter and wall thickness 0.1 cm is used to store hydrogen with an initial pressure of 8.7 atm. The tank is placed in outer space at
Ficks First Law
J = D c x
J flux of diffusing particles (molecules, atoms, ions, point defects, free electrons, electron holes, etc.). Flux has a direction. c x concentration gradient. D diffusion co
MatSc503 Kinetics of Materials Processes
Class time: Mon., Wed., and Fri. 2:30-3:20PM Class Room: 104 Steidle
Courseweb: http:/www.courses.psu.edu/courseweb/courses/index.cgi?course=matsc503_lqc3
Inst
Simultaneous Ordering and Phase Separation
'
+'
Ni
Al
Atomic structure
microstructure
Turbine Blade
Nucleation and Growth
G
Continuous transformations
Gn
Gg
Go
G p
A
BA
Microscopic diffusion equatio
MatSc 503 Kinetics of Materials Processes Spring 2000 Problem Set #6, Due April 19 1. A given phase transformation, to , occurs by nucleating cuboidal precipitates of from the matrix at 700 K. If the
MatSc503 Kinetics of Materials Processes Problem Set #5 Due April 5 1. Two similar carbon-saturated molten pig irons, one containing 0.8% S and the other 0.8% S and 0.46% Si, are in separate experimen
MatSc503 Kinetics of Materials Processes HW 2
Due February 2, 2000
1. 1-7 in Shewmon: It is suggested that the change in hydrogen potential of an aqueous solution could be measured by the change in el
MatSc503 Kinetics of Materials Processes
Due January 26, 2000
1. 1-2 in Shewmon 2. Part b of 1-4 in Shewmon 3. On silicon uniformly doped with 1015cm,3 atoms of arsenic, a very thin layer strongly dop
Solution to Problem Set #9 Problem 1. (a) Metal, M, undergoes an allotropic phase transformation between and at 1100 K. The low temperature phase is . A sample of M containing 108 cm-3 small oxide inc
Matsc 503 Kinetics of Materials Processes Spring 2002 Problem Set #9 Due: optional 1. (a) Metal, M, undergoes an allotropic phase transformation between and at 1100 K. The low temperature phase is . A
Solution to Problem Set #8 Problem A binary system A-B exhibits the regular solution behavior in the solid state. Answer parts (a) through (e), each when, o=(1/a)(da/dXA), the linear strain per unit c
Matsc 503 Kinetics of Materials Processes Spring 2002 Problem Set #8 Due April 17 A binary system A-B exhibits the regular solution behavior in the solid state. Answer parts (a) through (e), each when